Premium
The Jacobson radical of rings with nilpotent homogeneous elements
Author(s) -
Smoktunowicz Agata
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn086
Subject(s) - jacobson radical , mathematics , homogeneous , nilpotent , locally nilpotent , pure mathematics , algebra over a field , nilpotent group , combinatorics , ring (chemistry) , chemistry , organic chemistry
A result of Bergman says that the Jacobson radical of a graded algebra is homogeneous. It is shown that while graded Jacobson radical algebras have homogeneous elements nilpotent, it is not the case that graded algebras all of whose homogeneous elements are nilpotent are Jacobson radical. To contrast this, the following result of the author is slightly extended. Let R be a graded algebra generated in the degree one. If for every n , the n × n matrix algebra over R has all homogeneous elements nilpotent, then R is Jacobson radical.